The Standard Atmosphere · heat rises, and that is the point
The Air That Cools Itself
Heat rises. So why is it colder up a mountain? Because those are the same fact, not a contradiction. The rising air lifts into thinner air, expands, and pays for that expansion out of its own heat, so it cools as it climbs. For dry air the rate is exact and constant, about 9.8 °C per kilometre, and it falls straight out of gravity divided by the heat capacity of air. Lift a parcel up the slope below and watch its pressure drop, its bubble swell, and its temperature fall.
And no, you are not closer to the Sun in any way that matters. Grab the parcel at base camp, drag it to the summit, and read the two numbers side by side: a few kilometres nearer a Sun a hundred and fifty million kilometres away, against the tens of degrees the air has actually lost. Every value here is computed in your browser from the equations, and audited by an offline verifier that recomputes each one two independent ways.
Altitude z
0 m
at base camp
Pressure P
101.3 kPa
hydrostatic column
Volume V
×1.00
bubble swells as P falls
Temperature T
15.0 °C
dropped 0.0 °C from base
Drag the bubble on the mountain, drag this slider, or focus it and use the arrow keys. Everything to the right recomputes as it climbs.
DRY runs the constant 9.8 °C/km. MOIST cools dry until cloud forms at the LCL, then gentler as latent heat is released.
The temperature of the air at the foot of the mountain (sea level here).
How humid the base air is. The bigger the gap below the temperature, the higher the cloud base rides up the mountain.
Sound is off until you switch it on (a browser gesture is required), and it plays only quiet, synthesized tones: a soft pitch that falls as the parcel cools. Turn your device volume down first; there is nothing loud here, and no audio file is ever loaded.
Where the 9.8 comes from: the pressure cancels
Two facts about a rising parcel, multiplied together, and the pressure drops out, leaving a pure constant:
It is a constant for dry air: independent of temperature, and of how fast the parcel rises. The underlying adiabat the instrument runs is the Poisson relation P·Vγ = const with γ = cp/cv = 1004/717 ≈ 1.40 (7/5), equivalently T ∝ PR/cp with R/cp = 287.05/1004 ≈ 0.286 (2/7). Assumption named: dry, ideal-gas, hydrostatic air.
You are not closer to the Sun
The reflex wrong answer is "you are nearer the Sun up there." You are. It is also utterly negligible, and it points the wrong way: nearer the Sun means very slightly more sunlight, that is, warmer, not colder. Here are both effects at your current altitude, in the same units, computed live.
The two numbers, at z = 0 m
Warming from being closer to the Sun
+0.0 °C
you are – km nearer; sunlight up –%
Actual cooling of the air (environmental)
−0.0 °C
6.5 °C/km × height climbed (ISA)
Drag the parcel up to compare.
1 AU = 149,597,870.7 km (IAU 2012). Sunlight follows an inverse-square law, so the flux change is about twice the fractional distance change; a quarter of that fractional change is the equilibrium temperature response (Stefan-Boltzmann, T ∝ S1/4, at 288 K). Even Earth's whole perihelion-to-aphelion swing of ~5 million km barely moves the climate; a mountain's few km is a rounding error on that.
The deeper reason the whole column is cold
The parcel cools itself. The column is cold because it is heated from below.
Adiabatic expansion explains why a rising parcel cools. It is not, by itself, the whole reason the mountaintop is cold. The standing temperature gradient you actually meet, the environmental lapse rate averaging about 6.5 °C/km, is set by radiative-convective equilibrium. The atmosphere is nearly transparent to incoming sunlight, so it is heated from the bottom: the ground absorbs the Sun, warms, and warms the air above it by contact, convection and infrared, while the air loses heat to space from the top. Convection then stirs that heated-from-below air toward an adiabatic profile. The observed 6.5 is the compromise between the dry adiabat (9.8), the moist adiabat (about 5, wherever air is rising and raining out its moisture), and radiation. So the complete answer: "heat rises" is true; the rising air cools itself by expansion at 9.8 °C/km when dry, less where it condenses; and the reason the whole column is colder up high is that it is heated from below and stirred toward that lapse rate, not that each parcel simply rose and chilled, and not, by a factor of millions, that you got closer to the Sun.
Flip the toggle to MOIST and lift the parcel again. It cools at the full 9.8 until a cloud puffs onto the bubble at the lifting condensation level, then cools more gently as latent heat is released back into it. Turn on the three reference lines to see why the real 6.5 sits between the dry and moist adiabats: it is a mix, an average, not a law. Here are the three rates, kept distinct.
| Lapse rate | Value | Constant? | What it is |
|---|---|---|---|
| Dry adiabatic | 9.8 °C/km | yes, exactly g/cp | a rising unsaturated parcel, cooling itself by expansion |
| Moist / saturated | ~4–7 °C/km | no, varies with T and moisture | a saturated parcel, latent heat paying part of the bill; gentler low and warm, steepening toward 9.8 up high |
| Environmental (ISA) | 6.5 °C/km | no, an average that can even invert | the ambient air's own profile, the number you actually feel; a still cold morning can flip it so higher is warmer |
The check: every number recomputed in front of you
Nothing here is stored or fitted. For your current settings the page recomputes the whole ascent from the same equations the offline verifier uses, live:
Free choices & scope. Constants: g = 9.80665 m/s², dry-air cp = 1004 J/(kg·K) (1005 gives 9.76, both round to 9.8), R = 287.05 J/(kg·K), L = 2.5×106 J/kg, 1 AU = 149,597,870.7 km, Everest = 8,848.86 m (2020 survey). The parcel runs a dry-adiabatic, ideal-gas, hydrostatic column: pressure, volume, temperature and the Poisson relation are all mutually exact there. The saturated rate uses the standard formula with the Bolton (1980) saturation vapour pressure and a fixed L; real moist adiabats vary with the exact thermodynamics. The 6.5 environmental line is the ISA average, not a law: on a given morning an inversion can make higher air warmer. The snowline shown is the freezing level (0 °C isotherm) only, and is illustrative: a real permanent snowline depends on precipitation and latitude too, so no global snowline is computed from temperature alone. The offline gate recomputes all of it: node research/why-is-it-colder-at-the-top-of-a-mountain/verify-why-is-it-colder-at-the-top-of-a-mountain.mjs.
What is exactly true here, and what is a model
Exactly true (the sourced physics). "Heat rises" and "the top is cold" are the same fact: a rising parcel moves to lower pressure, expands, and cools. For dry air the rate is dT/dz = -g/cp, a constant derived by combining hydrostatic balance dP/dz = -ρg with the adiabatic first law cpdT = (1/ρ)dP, in which the density cancels. Numerically g/cp = 9.80665/1004 = 9.77 ≈ 9.8 °C/km. The ascent runs along the Poisson adiabat P·Vγ = const, γ = cp/cv ≈ 1.4. Once the parcel saturates, latent heat release gives a gentler, variable saturated rate (about 4 to 7 °C/km). The ISA environmental average is 6.5 °C/km, reaching -56.5 °C at 11 km from 15 °C at sea level. The distance-from-Sun effect is real, tiny, and of the wrong sign.
A model, not a measurement (the numbers). The pressure shown is the hydrostatic pressure of the parcel's own dry-adiabatic column, which is within a few percent of the standard atmosphere at low levels but is an idealization, not a specific day's barometer. The saturated branch integrates the standard formula numerically; the exact moist adiabat depends on details (ice vs liquid, the temperature dependence of L) that we hold fixed. The lifting condensation level uses the textbook estimate that the temperature-dewpoint spread closes at about 8 °C/km, giving roughly 125 m of height per °C of spread.
Named simplifications. Dry, ideal-gas, hydrostatic air; a fixed latent heat; the freezing level stands in for an illustrative snowline; the environmental line is an average, not a forecast. None of these change the reversal at the heart of the page: rising air cools itself, and that, not the Sun's distance, is why it is colder up a mountain.